INTERACTION PROBLEMS OF ACOUSTIC WAVES AND ELECTRO-MAGNETO-ELASTIC STRUCTURES

摘要

In the paper, is consider a three-dimensional model of fluid-solid acoustic interaction when an electro-magneto-elastic body occupying a bounded region ? + is embedded in an unbounded fluid domain ? ? = R 3 ?+. In this case in the domain ? + is a five-dimensional electro-magneto-elastic field (the displacement vector with three components, electric potential and magnetic potential), while in the unbounded domain ? ? is a scalar acoustic pressure field. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. In the paper, less restrictions are considered on matrix differential operator of electro-magneto-elasticity and asymptotic classes are introduced. In particular, corresponding characteristic polynomial of the matrix differential operator can have multiple real zeros. With the help of the potential method and theory of pseudodifferential equations, for above mentioned fluid-solid acoustic interaction mathematical problems the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces.